Question

Question Help A number of stores offer film developing as a service to their customers. Suppose that each store offering this service has a cost function (C) Cia) = 32 0.204 +0.12500? and a marginal cost (MC) MC) = 0.20 +0.2500 the going role for developing a roof fm is 750, the industry in long-run equilibrium? No Find the price associated with long-run equilibrium The market will be in long-run equilibrium when the price is $420(Enter your response rounded to two decimal places) Suppose now a new technology is developed that wil reduce the cost of fim developing by 20 percent. Assuming that the industry is in long how much would anyone or be willing to pay to purchase e chnology? Assuming that the market price remains at the above longeun equilibrium level, a firm would be willing to pay for the new technology (Enter your response rounded to two decimal places)

Answer 1

Given,

C = 32 +0.29 + 0.1250

MC = 0.2 +0.259

In the long run all the firms will be earning zero economic profit. The price is set at $ 7.50. The firm will maximize profit at P = MC

MC = 0.2 + 0.25q

=> 7.50 = 0.2 + 0.25q

=> 0.25q = 7.30

=> q = 29.2 units

Profit = 7.5 × 29.2 - (32+0.2×29.2 + 0.125×29.2² ) = $ 74.58

Profit is greater than zero hence the industry is not in the long run equilibrium.

In the long run equilibrium the industry is at equilibrium and the MC is equal to AC.

32+ 0.29 + 0.12502 AC =

Now, equate it to MC

32 +0.2q +0.1250 = 0.2+0.252

32 +0.29 + 0.12592 = 0.2q +0.2592

0.125q2 = 32

32 aq = 0.125

256 = ي ج-

q=1256

合1= 4256

q cannot be negative.

::9= 16

P = MC = 0.2 + 0.25×16 = $ 4.2

The market will be in long run equilibrium when price is $4.20

C. New technology reduces the cost by 20%. Then the new cost curve will be 80% of the original cost curve.

C = 0.8(32 +0.2q+0.12507

C = 25.6 + 0.16q+0.19

New marginal cost curve will be, MC = 0.16 + 0.2q

Price remains the same that is $ 4.20. the firm will set MC equal to Price that is $ 4.20

0.16 + 0.2q = 4.20

=> 0.2q = 4.04

=> q = 20.2 units

Profit = 4.2 × 20.2 - (25.6 + 0.16 ×20.2 + 0.1×20.2² ) = $ 15.204

New profit = $ 15.20

Therefore, a firm would be willing to pay $ 15.20 for the new technology.

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